# How many local extrema can a cubic function have?

Simple answer: it's always either zero or two.

To get a little more complicated:

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A cubic function can have up to 2 local extrema.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x/(x+9)# on the interval [1,4]?
- Is #f(x)=(6x^2-x-12)/(x+3)# increasing or decreasing at #x=3#?

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